Perhaps means maybe, or possibly. When you say something will perhaps happen, you're saying it might occur but you're not certain. If your friend asks whether you can come over this weekend and you reply “perhaps,” you mean there's a chance but you need to check first or see how things unfold.

The word suggests a thoughtful kind of uncertainty. When a scientist says her theory is perhaps correct, she's being careful and honest about what she knows and doesn't know. When a character in a story wonders perhaps the mysterious footprints belong to a fox, she's considering one possibility among several.

Perhaps sounds more formal and considered than “maybe.” You might say “maybe” casually to a friend, but you'd use perhaps when writing a careful essay or speaking respectfully to an adult. A weather forecaster might announce, “It will perhaps rain tomorrow,” meaning rain is possible but not guaranteed.